Systems and methods for analyzing building operations sensor data

ABSTRACT

Systems and methods are disclosed for analyzing building sensor information and decomposing the information therein to a more manageable and more useful form. Certain embodiments integrate energy-based and spectral-based analysis methods with parameter sampling and uncertainty/sensitivity analysis to achieve a more comprehensive perspective of building behavior. The results of this analysis may be presented to a user via a plurality of visualizations and/or used to automatically adjust certain building operations. In certain embodiments, advanced spectral techniques, including Koopman-based operations, are employed to discern features from the collected building sensor data.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation under 35 U.S.C. Section 120 ofco-pending and commonly-assigned U.S. Utility patent application Ser.No. 13/198,387, filed on Aug. 4, 2011, by Igor Mezic and Bryan A.Eisenhower, entitled “SYSTEMS AND METHOD FOR ENERGY EFFICIENT BUILDINGDESIGN AND MANAGEMENT,” which application claims the benefit under 35U.S.C. Section 119(e) of co-pending and commonly-assigned U.S.Provisional Patent Application Ser. No. 61/371,432, filed on Aug. 6,2010, by Igor Mezic and Bryan A. Eisenhower, entitled “SYSTEMS ANDMETHOD FOR ENERGY EFFICIENT BUILDING DESIGN AND MANAGEMENT,” both ofwhich applications are incorporated by reference herein.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with Government support under Grant No.DE-AC02-05CH11231 awarded by the Department of Energy. The Governmenthas certain rights in the invention.

TECHNICAL FIELD

The systems and methods disclosed herein relate generally to analyzingand decomposing building sensor information into a more manageable formto subsequently determine behavioral properties of a real or syntheticbuilding.

BACKGROUND OF THE INVENTION

Office buildings consume 40% of the energy used in the United States,and 70% of the electricity used in the United States. Energyconsumption, whether electrical, fossil fuel, or other energy usage, hasbecome a topic of concern, not only for efficient use of resources butalso for the global impact that energy consumption has taken on.

Since interest in efficient use of energy is high, technologies andtools that support the design of comfortable, clean, and efficientbuildings have been in use for many years. However, the inherent timeand length scales for such technologies and tools are generallyrelatively long (hours, days, large building spaces) and the performanceexpectations for these tools are averaged over time and large spatialdomains.

For example, occupants of a building are rarely interested in the finedetails of the temperature in a room as long as the temperature is keptwithin prescribed boundaries, while owners of the building are merelyinterested in keeping their overall monthly energy costs to a minimum.However, this situation changes dramatically when recent increases inenergy costs and concerns about environmental impacts are taken intoaccount.

Many existing efficiency-improving methods seek to achieve globalbuilding efficiency by optimizing individual building energy systemcomponents or subsystems. For example, more efficient compressors areused as retrofits for air conditioning systems, timed thermostats areused to anticipate building occupancy, or systems are given priorityrates from utility companies if the utility company can shut down orminimize energy deliveries in the event of a surge in energyrequirements in the area. Such approaches do not take a systems approachto building management or design, which would allow for even largersavings than retrofitting and variable usage conditions currently inuse. Accordingly, there is a need for a more comprehensive buildingenergy analysis system.

SUMMARY OF THE DISCLOSURE

Systems and methods are disclosed for analyzing building sensorinformation and decomposing the information therein to a more manageableand more useful form. Certain embodiments integrate energy-based andspectral-based analysis methods with parameter sampling anduncertainty/sensitivity analysis to achieve a more comprehensiveperspective of building behavior. The results of this analysis may bepresented to a user via a plurality of visualizations and/or used toautomatically adjust certain building operations. In certainembodiments, advanced spectral techniques, including Koopman-basedoperations, are employed to discern features from the collected buildingsensor data.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a cutaway perspective of a building comprising aplurality of environment affecting components and building sensors.

FIG. 2 is a floorplan for a building comprising a plurality of buildingsensors.

FIG. 3 is a generalized logical flow diagram illustrating how thebuilding sensor data analysis of certain of the embodiments may be usedfor presenting a visualization of building sensor data analysis to auser.

FIG. 4 is a generalized logical flow diagram illustrating how thebuilding sensor data analysis of certain of the embodiments may be usedin a building control feedback system.

FIG. 5 is a systems diagram illustrating the modular arrangement ofcertain embodiments of the GloBEMS software.

FIG. 6 is a time series plot of various building sensor data.

FIG. 7 is a generalized logical flow diagram illustrating how thebuilding sensor data analysis of certain of the embodiments may be usedto perform feature classification and data visualization.

FIG. 8 is generalized flow diagram illustrating various of the dataanalysis and processing techniques implemented by certain of theembodiments.

FIG. 9 is a plot of the frequency, or more generally, the Koopmanspectrum for a particular set of sensor data using a first visualizationtechnique.

FIG. 10 comprises a plot of the frequency, or more generally, theKoopman spectrum for a particular set of sensor data using a secondvisualization technique facilitating selection of data at individualfrequencies from an arrangement of values.

FIG. 11 is an illustration of an interpolated overlay upon a floorplanof the data selected for a frequency, or mode, from FIG. 10.

FIG. 12 depicts an interpolated overlay of the sensor data on afloorplan at a particular phase selected from the arrangement of FIG.10.

FIG. 13 depicts a generalized flow diagram for performing aKoopman-based analysis of the data.

FIG. 14 comprises a generalized systems diagram for modeling a physicalsystem as a series of inputs and a series of outputs.

FIG. 15 comprises a side-by-side comparison of a deterministic samplingtechnique and traditional sampling using a Monte Carlo technique.

FIG. 16 is a table depicting various levels of decomposition variablesin one possible sensitivity analysis.

FIG. 17 is a visualization of the results of a decomposition operationas used in certain embodiments in the form of a decomposed sensitivityweb.

FIG. 18 is a logical flow diagram general describing sensitivityanalysis as used in certain embodiments.

DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS

Modern buildings may include a variety of sensors to monitor thebuilding's environment and energy usage. Despite the plethora ofinformation these sensors provide, organizing this vast amount of datain a coherent manner can be a daunting task. Computer simulations ofexisting buildings or buildings yet to be constructed may similarlyinclude a vast amount of data, the useful information of which isdifficult to extract. Where these simulations incorporate data from bothreal-world and computer-simulated building sensors it may be especiallydifficult to extract meaningful information from the sensor results.

Certain of the present embodiments contemplate a sensor data analysissuite, comprising a plurality of data analysis tools, which facilitateefficient determination of relevant features in building sensor data.Particularly, the present embodiments improve the time, computationalpower, and reduce the level of user involvement necessary to determinefactors affecting energy efficiency. Certain embodiments of this globalbuilding energy management system make analysis of all parameters andoutputs of the building in question feasible, offering a building-wideoptimization result, where even only a general understanding of thebuilding's behavior may previously have been impossible.

FIG. 1 illustrates a cutaway perspective 100 of a building 101comprising a plurality of environment and energy affecting components,as well as various building sensors configured to monitor the building'sbehavior. Particularly, the building may comprise electric, gas, andheating components 102, cooling towers 104, lighting 103, water systems109 and other utilities. Some components such as the cooling coils 105,fans 106, and chillers and boilers 107, may be operated to adjust theinternal temperature of various rooms of the building 101. Sensors, suchas thermostats and humidistats, may be present and operate locallywithin the building. Some sensors may transmit their data to and beactivated from a central office or control system.

FIG. 2 illustrates a floorplan 201 of a building such as building 101.Although shown here as a two-dimensional, top-down view of a singlefloor, one will recognize a plurality of other possible representations,including a three-dimensional depiction of a multi-story architecture.Illustrated on the floorplan 201 are the locations of a number ofsensors 202 a-c. Each of these sensors may measure a plurality ofproperties of the building at their particular location, referred toherein as a “physical field”. A “physical field” may comprise anenvironmental aspect, such as temperature or humidity, but may alsocomprise a system aspect such as power consumption or electrical flow.The physical field sensor readings may be converted to an appropriateform to facilitate analysis. For example, a sensor may record change intemperature, or change in humidity, or may instead record an integral ofthese values over a period of time. Alternatively a computer system canperform this post-processing on the raw sensor data. Sensors may, forexample, measure physical fields such as temperature, humidity, airflow, electric power, occupancy, light, smoke, and/or any other sensors,individually or used in combination. Each sensor may store informationlocally, but may also transmit the information to a central system.Those sensors which communicate their information may be wireless orwired. Certain embodiments contemplate the sensors comprising an ad hocinfrastructure facilitating the transmission of readings to a centralsystem. In certain embodiments comprising wireless sensors, routers maybe used to collect data from local sensors and pass them on to thecentral system.

The floorplan 201 and sensors 202 a-c may not reflect a physical,real-world, building and sensor layout, but may instead reflect asynthetic model of a building, such as a software model. Such a modelmay comprise a building to be constructed, or one which is alreadybuilt. In a synthetic floorplan each sensor may be simulated byextracting simulation values from the model over different simulationcycles. In some systems a combined, physical and synthetic system may beused. For example, in FIG. 2, real-world physical data may be taken fromreal-world sensors 202 a and 202 b. However, sensor 202 c may not existin the real world and may be substituted with a synthetic softwaresensor. Similarly, sensors 202 a-c may all physically exist, but mayacquire different data or data via different standards. A softwaresimulation can then be used to supplement the data between the sensorsto achieve uniform sensor readings.

Once the data has been acquired from sensors 202 a-c, it would bedesirable to infer aspects of the building's behavior based on themeasured physical fields. While a user, such as an architect or buildingoperator, could analyze the data directly it may be very difficult todiscern important behaviors without performing data processing. A dataprocessing system may comprise a computing device having a processor anda memory. This system may be in the form of a personal computer or acluster computer, and may involve computing devices in the computingcloud, or may be implemented as an embedded system, or in other formsthat contain the basic processing and memory units. Certain embodimentscontemplate data processing software which may run on the dataprocessing hardware. This software may comprise a spatial-spectralinformation module, a graph decomposition information module, and asensitivity analysis module described in greater detail below. Anoperator using this software may be able to discern building behaviorsthat would otherwise remain hidden by the sensor data's complexity.

FIG. 3 depicts a generalized logical flow diagram illustrating how thebuilding sensor data analysis of certain of the embodiments may be usedfor presenting a visualization of a building sensor data analysis to auser. The system begins by acquiring sensor data 302, either physical orsynthetically generated, from a building. The system then analyzes thesensor data 303. Analyzing the sensor data 303 may require transformingthe data to a form more amenable to analysis as described in greaterdetail below (using orthogonal decomposition, frequency-based analysis,etc.). The system may then produce a visual representation 304 based onthe analysis to provide a user with a clear conception of the building'sbehavior based on the one or more measured physical fields. A userreviewing this visual representation 304 may then manually adjust thebuilding design or the building operation to achieve a more desirablebuilding behavior.

FIG. 4 depicts another generalized logical flow diagram, this timeillustrating how the building sensor data analysis of certain of theembodiments may be used in a feedback system. Here the analysis is usedas part of a feedback process to automatically adjust the building'sbehavior. For example, when designing a building using syntheticsensors, the system of FIG. 4 may perform a simulation of the building'sbehavior, analyze the results 303, and then adjust the buildingconfiguration as part of a supervisory control process 404 to a moreoptimal design. This process may be performed iteratively until adesired stop condition is reached. In a real-world system, the processmay instead adjust a building control system parameter using a buildingcontrol system, which may comprise one or more actuators. For example,after analysis the system may establish a new activation pattern for theair conditioning in a particular room. Certain embodiments contemplateperforming only either visualization (FIG. 3) or automated control (FIG.4) while other embodiments contemplate performing both, possibly reusingthe same data analysis 303.

Certain of the present embodiments contemplate a unified software suitewhich facilitates certain of the observations and operations depicted inFIGS. 3 and 4. FIG. 5 depicts one embodiment of this software system,referred to as a Global Building Energy Management System (GloBEMS). Theenergy, referred to may comprise thermal, electrical, or any otherphysical field data provided by the sensors which is pertinent toevaluating the building's behavior. Furthermore, some data considered bythe system may be derived from sources other than sensors, such ascalendar information, building meeting schedules, and weatherinformation. The GloBEMS system may include methods and apparatuses forefficiently analyzing, visualizing and controlling building energy usageand for designing buildings that allow for more efficient energy usage.Such a system may be implemented in software, firmware, or hardware asdescribed in greater detail below.

The diagrammatic representation of the software system of FIG. 5 may begenerally divided into three modules. As discussed below, datacollection may involve collecting data from real-world physical fieldsensors 511 or by using a synthetic building energy model 510, or byusing a combination of the two. The sensor data and building energymodel data can be integrated using data assimilation techniques thatimprove model information quality. The second module, the dataprocessing module 502, may then transform the data acquired from thedata collection module 501 into a form more amendable for analysis. Thedata processing module 502 may then analyze the data. The analyzed datamay then be presented to a visualization and/or actuation module 503which either visualizes the data 531 or actuates certain buildingsystems 532 as described above with respect to FIGS. 3 and 4respectively.

An effective visualization or system modification requires that the databe properly analyzed. Certain embodiments contemplate using one or moreof a graph decomposition module 521, sensitivity analysis module 523,spectral-spatial decomposition module 522, including Koopman modemethods and energy-based (in some embodiments Proper OrthogonalDecomposition [POD]) methods, as described in greater detail below. Theresults of these modules may be provided to the visualization andactuation module 503 directly or may be first integrated via a systemintegration module 524. Particularly, information from graphdecomposition 521, spectral-spatial methods, including Koopman modemethods and POD methods 522, or sensitivity analysis and uncertainty andsensitivity analysis module 523 can be integrated and refined using thesystem integration module 524. The information from the data processingmodule may be used by the visualization and/or actuation module tovisualize the results of the data analysis or to take action basedthereon, respectively.

Certain embodiments contemplate further interactions between the GraphDecomposition Module 521, the Spectral-Spatial Decomposition Module 522,and the Sensitivity Analysis Module 523. Particularly, after the systemor a user has performed an analysis using the Spectral-SpatialDecomposition Module 522, certain embodiments contemplate using theresults to perform a sensitivity analysis using Sensitivity AnalysisModule 523 or a graph decomposition using Graph Decomposition Module521. In some embodiments, the system may iteratively perform asensitivity analysis or graph decomposition by performing aspectral-spatial analysis across a plurality of parameter values. Thatis, where a physical building is being studied, a parameter such aswindow shade length in the afternoon, may be set to one of a pluralityof values and the spectral-spatial analysis subsequently performed foreach of the values A sensitivity analysis may then be performed on theresultant modes. A similar process may occur for simulated building datafrom a synthetic model. The system or user may also perform iterativeanalyses using Spectral-Spatial Decomposition Module 522 and GraphDecomposition Module 521 in a similar manner. As indicated in thefigure, certain embodiments also contemplate the Sensitivity AnalysisModule 523 performing an analysis by interacting with the GraphDecomposition Module 521 directly.

One will readily recognize that not all of these modules need be presentin a single system and that certain implementations may omit or includeadditional modules than those shown. For example, the processingsoftware modules can also include energy models, flow models or anyother physical models that computes future states of physical variablesin a building. The processing software can contain modules thatinterlink, combine and additionally process any of the information insoftware modules described hereto.

Certain embodiments contemplate integrating the system 500 with a userinterface including a visualization device such as a computer terminal.Such a computer terminal could be located in public areas of thebuilding such as a lobby, business portions of the building such asoffices, stores, data centers and other or building operator offices.The actuation system could include at least one actuator capable ofactuating physical change in a system, such as change in mass, energy orlighting state of the system or providing occupants or operators withinformation that enables them to impose a physical change in thebuilding system, such as a visualization system that displays messagesof importance for energy control in a building.

Sensor Data Analysis—Overview

FIG. 6 illustrates an example dataset 601 for a plurality of sensors.For each sensor a data profile 602 a-c may be generated depicting thesensor's value 603 over time 604. In this particular example, thesensors record temperature values at periodic intervals. One willrecognize that the points may be interpolated between the sensor data tofacilitate a continuous dataset if the sensors take samples at differentperiods or with relative phase offsets. Similarly, data may beinterpolated for other reasons, such as when the sensors provide asparse dataset. While it is possible for a user to analyze buildingbehavior by visually inspecting raw sensor data as depicted 603, theyare likely to overlook certain important features.

FIG. 7 illustrates a general process by which sensor data may beconverted to a form more amenable to analysis by a user or by anautomated system. Initially, the raw sensor data 702 may be organizedinto a form for data manipulation. In some embodiments, records ofindividual sensor values over a time period of interest may be organizedinto a matrix and interpolation performed between values as necessary toachieve a complete dataset. This dataset may then be transformed 703 toa desired analysis form 704. In some embodiments this transformation 703may comprise a Fourier Transform, Koopman, or other spectral-basedtechnique. Generally speaking, methods such as the Fourier Transform andArnoldi Method may be used when only a subset of the Koopman Operator'seigenvalues and eigenvectors are desired. Where a more complete set ofeigenvalues and eigenvectors are desired, methods such as the Mezicmethod may be used. In some embodiments the transformation 703 may alsocomprise a POD (for example, Principal Component Analysis), or otherenergy-based analysis technique (one in the art will recognize theMori-Zwanzig formalism, optimal prediction, and other projectionmethods).

The transformed dataset 704 may then be used to generate 705 avisualization 706 of the sensor data results, as described above withrespect to FIG. 3. Generation 705 of the visualization 706 may occur inconjunction with a user-specified selection of a region of interest. Insome embodiments, the visualization may comprise an overlay as depictedin FIG. 7. Rather than produce a visualization the system may insteadanalyze the modified data 704 and adjust control behavior as discussedabove with respect to FIG. 4.

Sensor Data Analysis—Methods Overview

Certain of the present embodiments provide a suite of data analysistechniques from which a user or control system may select. FIG. 8depicts certain of the methods for generating data pursuant to thegenerally described process of FIG. 7. Particularly the embodimentsillustrated by FIG. 8 comprise energy-based suite of methods 810 and aspectral based suite of methods 820. The energy based suite may comprisetechniques, such as proper orthogonal decomposition (POD), (one willreadily recognize various characterizations of POD in the art, such asPrincipal Component Analysis (PCA), Karhunen-Loeve transform (KLT), orthe Hotelling transform). The frequency-based analyses may comprise theFourier Transform and Koopman methods implemented using, perhaps, theArnoldi or Mezic (harmonic averages of the spatial field) approachesdiscussed in greater detail below.

The system begins 801 by receiving the raw sensor data 802, possiblypre-processed and arranged into a suitable form. In some embodiments thereceived data may be organized as a matrix, wherein sensor values at aparticular instant in time are placed in each column or row. Asdiscussed above, interpolation between sensor values may be performed.Higher order matrices or tensors may likewise be used to organize moredetailed datasets, although the following description is with respect toa two-dimensional matrix for purposes of illustration.

Certain embodiments contemplate performing a plurality of analyses usingdifferent methods from each of the suites 810, 820, etc. An energy basedanalysis, such as the POD analysis may be selected and performed (asgenerally described in greater detail below). POD will generate aplurality of vectors, comprising values associated with each sensor at aparticular energy level. The user or the system may then select anenergy level of interest 812. The vectors associated with the selectedenergy level may then be used to generate a visualization 830 similar tothe overlay of FIG. 12 described in greater detail below at each oftheir respective sensors. As mentioned, the system may instead analyzethe selected energy level to determine an appropriate action to take.

Sensor Data Transformation—Proper Orthogonal Decomposition

As mentioned, in certain embodiments the sensor data may be transformedvia POD to a form more amenable for analysis. As POD comprises aplurality of decomposition techniques, the following description ismerely a generalization of certain embodiments for descriptive purposes.

During POD, the system may first receive the physical field data fromthe real, simulated, or partially real and simulated building sensordata. In some embodiments, the mean of the data may then be subtractedand the covariance matrix of the modified dataset calculated. Theeigenvalues and eigenvectors of this covariance matrix RR06 may then becalculated. Known techniques for the calculation or estimation ofeigenvalues, such as matrix decomposition (Support Vector Decomposition)or the Jacobi eigenvalue algorithm may be used. The eigenvalue with thehighest value may be termed the “principle component” and a totalordering of eigenvalues performed based upon their respectivemagnitudes. The eigenvectors corresponding to each eigenvalue may besimilarly ordered based upon the eigenvalue magnitudes. Each of theseeigenvectors may be referred to as a mode (the first mode being the“principle component”, etc.). Depending on the system configuration,some number of the largest eigenvectors may be selected to form a“feature vector”. The data is then projected onto this feature space toderive the POD features, or modes. The above is merely a general summaryof the POD process and one skilled in the art will readily recognizenumerous various and omitted details.

Thus, POD generates a plurality of real vectors (i.e., vectorscomprising real components) and the associated energy values(eigenvalues, or singular values). These vectors, or modes, may then beused in order to visualize the spatial location of dominant dynamicalenergy of the sensor data. To clarify, the “dynamical energy” or“spectral energy” of the sensor data is here referring to the “energy”in the signal in a signal processing sense. This energy may or may notbe correlated with, or the same as, the thermal, electrical, or otherphysical field energy in a building.

The system or user may then select an energy level and an associatedeigenvector to perform a visualization similar in appearance to FIG. 11.Particularly, each value from the vector is plotted in the overlay atthe spatial location of the corresponding sensor on the floor plan andmay be scaled appropriately as necessary. Interpolation between valuesmay then be performed to plot intermediate values between sensorlocations on the overlay. This may make it easier to determine buildingbehavioral properties and to distinguish faulty operation fromnon-faulty operation, specifically by identifying dynamical energycontent in a Proper Orthogonal Mode that is neither typical (wheretypical behavior may be established based on the measurement of theoperation of a building or by running an energy model) noruser-requested. Such information can also be used to design supervisorycontrollers. When faulty operation is identified at a spatial locationusing POD, actuators at that location may be instructed to performcorrective action.

Unfortunately, while POD is useful for determining some features of thedata it may not always lend itself to a comprehensive understanding ofthe building behavior. Particularly, the largest eigenvalues of theabove POD analysis indicate the highest energy modes of the transformeddataset. Organizing the data based on the highest mode may not always beuseful. These energies may comprise many different frequencies ofinformation that instead reflect anomalous behavior in the buildingoperation. Furthermore, each eigenvector of the POD may be orthogonal toits peers. Thus, in some instances, it may be more preferable to view ortake action based on the data after transforming the data to a formwhich facilitates more versatile reflection of the data contents,particularly including the frequency content. In certain embodiments, aspectral transformation, such as a Fourier or more generalizedKoopman-based analysis, provides this versatility.

Sensor Data Transformation—Spectral-Based Approach—Fourier Transform

The spectra and modal content of the data may reveal useful informationabout the content of the data especially when its origin is frombuilding sensors. Sensor faults, improperly installed or commissionedcontrol systems, and aging or dysfunctional equipment may be detected.Although Koopman and Fourier methods are discussed separately in thisdocument, one will readily recognize that the Fourier method comprises aspecific instance of the more general Koopman-based methods referred toherein.

Spectral analysis is also useful for the calibration of building models.Spectral analysis provides a quick way to determine the performance of abuilding and may therefore be used as a metric to determine thedifference in the performance of a model as compared to the performanceas seen in real-world data. Spectral analysis may be used tore-calibrate building systems models by comparing spectral modes ofmodel versus the data. If, for example, the phase response from themodel differs from what was seen in data, the model may bere-calibrated.

In certain embodiments, the Fast Fourier Transform (FFT) may be employedto determine the frequency character of the sensor data. In theseembodiments, the system may iterate through each sensor in the dataset821 and calculate the FFT for the sensor values over a selected period.One will readily recognize alternative methods for calculating theFourier Transform, such as by performing a multi-dimensional FFT of thedata. In either case, the Fourier Transform in certain embodiments willproduce a “mode” matrix comprising complex-valued entries (representingthe corresponding phase and magnitude). In these embodiments, a firstdimension of the matrix may correspond to each of the sensor values (Mrows in the matrix for M sensors). A second dimension of the matrix maycorrespond to a vector of frequencies also produced by the FourierTransform (N columns of the matrix for N frequencies). Thus, for amatrix comprising M rows and N columns (an M×N matrix), the matrixentries will represent the value of the Mth sensor associated with theNth frequency. Again, each of these entries will be complex to representthe phase and magnitude. In such an arrangement, each of the N columnsmay be referred to as a “mode”.

Also, each of the M rows may be separated from the matrix to produce a“frequency vector” for a sensor. The modes may similarly be separatedfrom the matrix. Thus, each column of the matrix will comprise the moderelated to the i^(th) frequency in the frequency vector. One willrealize that this arrangement is merely for the purposes of illustrationand that the same data can be organized differently.

Once the Fourier representation is acquired, the user or system may thenselect a frequency, or mode, of interest 824 (a column N of the matrix)and determine the corresponding vector or frequency values 825 (each ofthe M sensor entries for that column). The system can then determine themagnitude and phase for each sensor 826 based on the complex entries ofthe selected matrix row. This will generate a pair of values which maybe associated with each sensor. The system may generate a first plot 830for the magnitude and a second plot 830 for the phase. A discussion ofthe magnitude plot is made with reference to FIG. 11 and of the phaseplot with reference to FIG. 12. As previously discussed the system mayinstead take action on the analysis.

FIG. 9 depicts one possible visualization 900 of the sensor dataset'sspectral character, as determined by a method such as the FourierTransform. Here, the period 901, rather than the frequency has been usedto organize each sensor value. The magnitude of a value is depicted bythe vertical axis 904. Each circle 902 a-c represents a sensor valuecorresponding to a particular period/frequency, in this case 42hours/cycle 903. While the representation 900 of FIG. 9 is accurate, itmay be difficult for a human operator or automated system to ascertainthe building's behavior from such a visualization.

FIG. 10 depicts another possible visualization of a dataset's spectralcharacter, determined using, for example, the Fourier Transform or aKoopman-based approach. Here the sensor values are organized along thevertical axis, corresponding to the M rows of the generated matrix. Thefrequency/period is indicated along the horizontal axis, correspondingto the N columns of the generated matrix. Generally, the frequencyresolution may be restricted by the available data. However, algorithms,such as FFT, may provide parameters to specify the frequency grid forwhich calculations are to be performed. Additional methods forinterpolating between available datapoints will also be readily known toone in the art. For each entry 1010, the corresponding magnitude for asensor value is depicted by the intensity. In some embodiments, theintensity may be reflected in the hue or luminosity of the entry or by aheight if the visualization were presented in a 3D view. This threedimensional representation (sensors, period, and magnitude) facilitatesuser selection of the values associated with the sensors at a particularfrequency. For example, in certain software implementations, a user maymove a slider along the frequencies 1050A-C in a range 1060 and generatea corresponding visualization 1051A-C for all the sensors at each of theselected frequencies 1050A-C. By inspection of the visualization 1020, auser can identify anomalous spectral behavior, such as that indicated atthe entry 1010. The user may select the corresponding frequency 1050Aand generate the corresponding visualization 1051A.

One such visualization 1110 is depicted in FIG. 11. Having selected thedesired frequency, the system may iterate between each sensor value ofthe corresponding vector. These values may be assigned to each sensor1120A-D in an overlay on the building floorplan. Although illustratedhere as a two-dimensional floor plan, one will recognize that athree-dimensional representation may also be provided. The system maythen generate values between each of the sensors' 1120A-D values, suchas at pixel location 1140, by interpolating or averaging nearby sensors.In this example, the values corresponding to sensors 1120C and 1120D arequite high, whereas the neighboring values are much lower. This mayindicate an anomalous behavioral property, if the physical field atthese sensors' location is not intended to be active at the selectedfrequency. One will recognize the identified behavioral property asbeing any property correlated with a physical field of the building,such as temperature fluctuation, energy-usage fluctuation,electrical-activity fluctuation, etc. Determining such a behavioralproperty may involve an automated system recognizing the behavioralproperty from the above-processed data, or the property being presentedto the user as part of a visualization. In some embodiments, the sensorinfluence may be weighted by the distance from the pixel location 1140to the sensors. One will readily recognize that a similarinterpolated-overlay may be generated for any sensor-based collection ofvalues, such as the results of the POD analysis. Any physical field maybe plotted in this manner. For example, temperature, humidity, airflow,pressure, people occupancy, plug load density, light intensity, etc. mayall be overlaid on the floor plan of the building.

As mentioned, each complex entry of the matrix will facilitate bothmagnitude and phase information for the sensor. For these spectral-basedtechniques, a similar visualization to 1110 may be generated for thephase information of the sensor. FIG. 12 depicts a phase visualizationagain overlaid over a floorplan 1200. Here, each value associated with asensor indicates the phase difference between the sensor's data and areference frequency at the selected frequency 1050A. Certain spectraltechniques, such as the Fourier Transform, generally generate the phasewith respect to a reference of zero, or no phase. In some embodiments,the phase of the sensor data 1230 is instead calibrated relative to thefrequency of the ambient outdoor air temperature 1220. That is, if thesensor data has a phase relative to zero phase of 30 cycles, and theoutdoor air temperature has a phase relative to zero of 20 cycles, thesensor phase value used for generating visualization 1200 may be 10cycles. The user or system may select alternative references than theambient air temperature, such as a phase associated with the operationalhours of the building. In this manner the visualization 1200 will depictthe sensor relation to a basis of interest.

While the Fourier Analysis provides important information regarding thespectral character of the building sensor data, the system or user isconstrained to analyzing the spectral character according to theprinciples inherent to the transform.

The system or user may be better able to identify anomalous buildingbehavior or regions of interest if they had greater flexibility andcontrol over the character of the generated spectral content. Certainembodiments contemplate applying more sophisticated techniques, such asKoopman-based spectral techniques, than the Fourier Transform.Generally, Koopman analysis provides a less restrictive collection oftools for assessing the spectral character of a set of sensor data. Insome embodiments the Koopman character of the data is determined byapplying the Arnoldi, Mezic, or similar methods.

Sensor Data Transformation—Spectral-Based Approach—Koopman-OperatorBased Spectral Methods

The Koopman operator is an infinite-dimensional linear operatorassociated with a full nonlinear system. Particularly, consider adynamical system evolving on a Manifold M, such that, for x_(k)<M,

x _(k)+1=f(x _(k))  (1)

where f is a map from M to itself, and k is an integer index. As anexample, the manifold M may comprise the entire universe of possiblesensor values for a collection of sensors. The system as a whole maypossess state x_(k) at time k and subsequently x_(k+1) at time k+1. Themap, or function f, is then indicative of the means by which the systemtransitions from each successive state, i.e. between each set of sensorvalues. The Koopman operator is a linear Operator U that acts onscalar-valued functions on M in the following manner: for anyscalar-valued function g: M->R, U maps g into a new function Ug give by

Ug(x)=g(f(x))  (2)

By virtue of the operator's ability to relate these functions in thismanner, the operator possesses important information about the nature ofthe function f. Were the operator determined for the function associatedwith a building, it would yield important information regarding thequalities of that building. Unfortunately, although the dynamic systemis nonlinear and evolved on a finite-dimensional manifold M, the Koopmanoperator U itself is infinite dimensional. Thus, computing the KoopmanOperator itself, exactly, is generally intractable. Furthermore,building systems usually comprise large sets of sensor data x_(k),x_(k+1), x_(k+2), etc. and the function f describing this relationshipis usually extremely complex and unknown.

Thus, it would be desirable to analyze the system information containedin the Koopman Operator, but using only available data-collected eithernumerically or experimentally and without having to calculate theOperator explicitly. Certain of the present embodiments contemplateinstead calculating the eigenfunctions and eigenvalues of the KoopmanOperator U and using these as a basis for analysis of the system.Furthermore, these embodiments employ methods for deriving theeigenfunctions and eigenvalues from only a finite, known set of data.Let φ_(p) denote the eigenvectors or eigenfunctions of the KoopmanOperator (referred to herein as Koopman eigenfunctions) and lettingλ_(j) denote the eigenvalues (referred to herein as the Koopmaneigenvalues), then:

Uφ _(j)(x)=λ_(j)φ_(j)(x), j=1,2,3  (3)

The known dataset may then be characterized as a vector-valuedobservable q:M->Rp. That is, a collection of values from the universe ofpossible values. The observable q may be projected upon the Koopmaneigenvectors to retrieve the desired spectral information. The datasetmay then be represented in terms of its components relative to theKoopman Eigenspace, i.e. as:

$\begin{matrix}{{q(x)} = {\sum\limits_{j = 1}^{\infty}\; {{\phi_{j}(x)}v_{j}}}} & (4)\end{matrix}$

Where v_(j) are a linear combination of vectors representing thecomponent of q(x) along that component of the Koopman eigenvector, orsometimes referred to as an eigenfunction, φ_(j). Some embodiments referto these vectors as “Koopman modes” of the data. Thus, the Koopmaneigenvalues λ_(j) characterize the temporal behavior of thecorresponding Koopman mode v_(j). The phase of λ_(j) determines thefrequency, and the magnitude determines the growth rate. The Koopmaneigenvalues characterize the temporal behavior of the correspondingKoopman mode. The Koopman modes may be plotted visually in a similarmanner to the Fourier Transform as was discussed in relation to FIG. 11.

Calculation of the Koopman eigenvectors and eigenvalues may beaccomplished by a variety of methods, including the Arnold algorithm,variations of the Jacobi method, and the Mezic method described ingreater detail below. Qualities of the Koopman operator's spectra may beused to quickly highlight inconsistencies in controller function. As wasdiscussed with regard to the Fourier Transform, investigating theKoopman modes generally comprises computing the spectra of the Koopmanoperator and then selecting a particular frequency of interest. TheKoopman mode associated with the selected frequency may then be obtainedand investigated. Koopman mode information further allows users toquickly quantify whether these very important parts of the buildingdynamics are properly set up in the model. This may facilitate theidentification of differences between predictions and measurements andthus to highlight performance issues with the building. Insights basedon the magnitude and phase information may also be used to improve acorresponding simulation model. Koopman-based methods are well suitedfor dynamics which contain significant amounts of periodic content.Koopman methods facilitate quick conclusions regarding sensor functionand may also be used to compare models and real-world data more quickly.A complete description of the Koopman operator may be found in “SpectralAnalysis of Nonlinear Flows” Rowley, et al., Journal of Fluid Mechanics(2009), 641: 115-127, incorporated by reference herein.

FIG. 13 illustrates a generalized flow diagram for performing aKoopman-based analysis of the data. Koopman-Based operations 821 asfound in certain implementations of the suite of spectral techniques820. Generally, these Koopman-based operations will determine theeigenspace 1301 (the collection of eigenfunctions) of the KoopmanOperator of the dataset based on one of a plurality of methods(discussed in greater detail below). The system may then project 1302the original dataset onto this determined eigenspace, in someembodiments by taking the inner product. This will produce the spectraldata from which a frequency of interest 824 and associated visualizationmay be produced. Although depicted in FIG. 13 as two separate steps, onewill readily recognize that the computational implementation may performthese operations simultaneously or in effect via other operations.

Calculation of Koopman Modes—Arnoldi Method

The following disclosure presents one possible algorithm, the ArnoldiMethod, for computing Koopman modes given only values of a particularobservable (snapshots), sampled at regular times. Data from real-worldsensors may regularly be in the form of these snapshots. We assume thatfor any state x, w may measure a vector-valued observable g(x)εR^(p). Inparticular, the Arnoldi algorithm, when applied to a nonlinear system,produces approximations to eigenvalues of the Koopman operator and theircorresponding modes.

The following discussion provides an example version of the Arnoldialgorithm which operates on a linear system and does not requireexplicit knowledge of the underlying operator A. However, certainembodiments contemplate an alternative interpretation of the algorithmthat applies to nonlinear systems, and connects with the Koopman modes.Applications of the Arnoldi method in a nonlinear context are alsodiscussed in “Spectral Analysis of Nonlinear flows” Rowley, et al.,Journal of Fluid Mechanics (2009), 641: 115-127, incorporated byreference above.

Example Arnoldi Algorithm for Linear Systems

The following is a general discussion of certain aspects of the Arnoldialgorithm as may be applied in certain of the embodiments. Consider alinear dynamical system

x _(k+1) =Ax _(k)  (5)

where x_(k)εR^(n), and n is so large that we cannot compute eigenvaluesof A directly. Certain embodiments compute estimates of theseeigenvalues using the Krylov method, in which one starts with an initialvector x₀ (often chosen to be a random vector), and computes iterates ofx₀. After m−1 iterations, one has a collection of m vectors that span aKrylov subspace, given by span {x₀, Ax₀, . . . , A^(m-1)x₀}. Certainembodiments then approximate eigenvalues and eigenvectors by projectingA onto this m-dimensional subspace, and computing eigenvectors andeigenvalues of the resulting low-rank operator. The data vectors may bestacked into an n×m matrix

$\begin{matrix}\begin{matrix}{K = \left\lbrack {x_{0}\mspace{14mu} {Ax}_{0}\mspace{14mu} A^{2}x_{0}\mspace{14mu} \ldots \mspace{14mu} A^{m - 1}x_{0}} \right\rbrack} \\{= \left\lbrack {x_{0}\mspace{14mu} x_{1}\mspace{14mu} x_{2}\mspace{14mu} \ldots \mspace{14mu} x_{m - 1}} \right\rbrack}\end{matrix} & (6)\end{matrix}$

then we wish to find approximate eigenvectors of A as linearcombinations of the columns of K. The Arnoldi algorithm is a type ofKrylov method in which one orthonormalizes the iterates at each step,and it therefore involves computing the action of A on arbitraryvectors. A variant of this algorithm that does not require explicitknowledge of A is given below.

First, consider the special case where the m-th iterate xm is a linearcombination of the previous iterates. We may write

x _(m) =Ax _(m-1) =c ₀ x ₀ + . . . +c _(m-1) x _(m-1) =Kc  (7)

where c=(c₀, . . . , c_(m-1)). Thus, we have

AK=KC  (8)

where C is a companion matrix given by

$\begin{matrix}{C = \begin{matrix}0 & 0 & \ldots & 0 & c_{0} \\1 & 0 & \; & 0 & c_{1} \\0 & \; & \; & \; & c_{1} \\\vdots & \; & \ddots & \; & \vdots \\0 & 0 & \ldots & 1 & c_{m - 1}\end{matrix}} & (9)\end{matrix}$

The eigenvalues of C are then a subset of the eigenvalues of A: if

Ca=/λa  (10)

then using (8), one may verify that v=Ka is an eigenvector of A, witheigenvalue λ.

More generally, if the m-th iterate is not a linear combination of theprevious iterates, then instead of the equality (7), we have a residual

r=x _(m) Kc  (11)

which is minimized when c is chosen such that r is orthogonal to span{x₀, . . . , x_(m-1)}. In this case, the relation (3.5) becomesAK=KC+re^(T), where e=(0, . . . , 1)εR^(m). The eigenvalues of C arethen approximations to the eigenvalues of A, called Ritz values, and thecorresponding approximate eigenvectors are given by v=Ka, called Ritzvectors. Note that the full Arnoldi method is more numerically stablethan this method, and reduces A to an upper Hessenberg matrix, ratherthan a companion matrix.

As mentioned with regard to FIG. 13, an important feature of the abovealgorithm is that it does not require explicit knowledge of the matrixA: all it requires is a sequence of vectors, as summarized below.

Consider a sequence {x₀, . . . , x_(m)} where x_(j)⊂R_(n). Define theempirical Ritz values λ_(j) and empirical Ritz vectors v_(j) of thissequence by the following algorithm:

Define K by (3.3) and find constants c_(j) such that

$\begin{matrix}{{r = {{x_{m} - {\sum\limits_{j = 0}^{m - 1}\; {c_{j}x_{j}}}} = {x_{m} - {Kc}}}},{r\bot{{span}\left( {x_{0},\ldots,x_{m - 1}} \right)}}} & (12)\end{matrix}$

Define the companion matrix C by (3.6) and find its eigenvalues andeigenvectors

C=T ⁻¹ ΛT, Λ=diag(λ₁, . . . , λ_(m)),  (13)

where eigenvectors are columns of T⁻¹.

Define v_(j) to be the columns of V=KT⁻¹:

If x_(j)=A^(j)x₀, then the empirical Ritz values λ_(j) are the usualRitz values of A after m steps of the Arnoldi method, and v_(j) are thecorresponding Ritz vectors. These, may provide good approximations ofthe eigenvalues and eigenvectors of A. However, if we do not havex_(j)=A^(j)x₀ (for instance, if the sequence is generated by a nonlinearmap), then at this point, it is not clear what the above algorithmproduces. For a nonlinear system, the algorithm produces approximationsof the Koopman modes and associated eigenvalues. A correspondingdescription for nonlinear systems may be found in (See, e.g. “SpectralAnalysis of Nonlinear flows” Rowley, et al., Journal of Fluid Mechanics(2009), 641: 115-127), incorporated herein by reference.

In addition to the Arnoldi method, one skilled in the art will befamiliar with other methods for calculating the Koopman Operator, suchas those of Mezic, et al. A general discussion of the Mezic approach maybe found in “Spectral Properties of Dynamical Systems, Model Reductionand Decompositions” Igor Mezic, Nonlinear Dynamics (2005) 41:309-325,incorporated herein by reference.

Parameter Sampling and Sensitivity Analysis

While the above spectral and energy-based methods may be used todetermine characteristics of a sensor dataset, effectivecharacterization of building behavior may also depend on selectingappropriate sensors and appropriate physical fields from which tocollect data. Thus, independently or in conjunction with theabove-described methods for data transformation and analysis, certain ofthe present embodiments contemplate a building management system whichalso identifies pertinent sensors and physical fields for analysis usinga model of the building and certain decomposition methods described ingreater detail below. A combined Koopman Analysis-Decomposition methodis also discussed in greater detail below.

FIG. 14 illustrates a system 1403 which receives a plurality of inputs1401A-D and produces a plurality of outputs 1402A-B. System 1403 hererepresents a synthetic, computer model of a building, such as by usingone of the Energy Plus, TRNSYS, or Equest models known to one skilled inthe art. By varying inputs 1401A-D and monitoring the effect on outputs1402A-B the relationships between the inputs and between the inputs andthe outputs may be determined.

Decomposition methods comprise methods for reducing a complexarrangement of data to a more useful form, by recognizing which datacomponents most greatly influence one another or one or more physicalfields of interest. In the context of building efficiency, energyefficiency and environmental protection goals may be affected by a widevariety of distributed components in a system. Structural elements,communication systems, sensing systems, transportation systems, airquality systems, and power systems of a building may interact in ahighly complex manner. The behavior of these components may be modeledin software. These energy simulation tools may comprise a suite ofdetailed physical relations (differential, algebraic, etc.) thatdescribe the way various disturbances (from weather, humans, controlsystems, etc.) influence the thermodynamic behavior of a building.Within these equations, thousands of parameters, or inputs, may exist.At times these values may be supplied by the best-educated guesses of ananalyst. Unfortunately, parameter errors may cause a tool whichaccurately represents real-world behavior to produce erroneous results.

With respect to FIG. 14, it would be desirable to select a range ofvalues for each input 1401A-D and an associated granularity. Then,computer simulations may be run at each of the input value iterationsand the resulting outputs observed. For example, for an input comprisingthe length of a window shade, the range would be the distance in feetfrom no extension (0 feet) to full extension (4 feet) of the windowshade. As the range from 0-4 comprises an infinite number ofintermediate values, the analyst may select discrete values for aparticular granularity. For example, a granularity of one foot may beselected so that the collection of input values considered is 0, 1, 2,3, and 4 feet. For all the inputs, an analyst may iterate between eachof these values and run a corresponding simulation to generatecorresponding outputs 1402A-B. By observing the outputs 1402A-B wheniterating through every possible combination of input values, theanalyst may infer relations between each of the inputs and between theinputs and the output. In some simulations not all parameters changeindividually (one at a time). In others, the parameters may change allat once (which may be more efficient computationally). Certain systemsmay adjust the granularity as yet another input to determine how themodel reacts, and need not select an evenly distributed granularitywithin the range as in this example.

In fact, as the choice of parameter range and distribution willinfluence the sampled behavior of the building model, certainembodiments consider selecting ranges and distributions usingpseudo-random and random techniques. FIG. 15 illustrates the results ofa deterministic sampling method using traditional sampling techniques1501 as compared to using a random technique, such as Monte Carlo 1502.Certain of the present embodiments contemplate using either samplingmethod.

In deterministic sampling, instead of randomly selecting the next pointto sample, an equation may be used to find the next sample point. Suchan equation can be written as

x′=T(x)  (14)

where x′ denotes the next sampling location and T(x) describes a mappingof the previous sampling location x. If such mapping T is uniformlyergodic, then good convergence properties of sampling may be obtained.Random sampling methods instead select the next point using a randomnessalgorithm such as Monte Carlo. In the traditional methods (Monte Carlo),clumping may occur in the sampling approach. These clumped sampledpoints may indicate inefficiency in the sampling approach and waste timein the analysis of the building design. Latin hypercube sampling (LHS)may be used to initially partition the space into equally probable areasprior to taking random samples to avoid this problem.

Certain embodiments combine the use of Monte Carlo and Quasi-Monte Carlo(i.e. deterministic) methods which may be much faster and more exactthan using Monte Carlo methods alone. Quasi-random sampling methods mayprovide a faster convergence rate and fewer simulations to obtain thesame accuracy that other methods offer. This may allow more uncertainparameters to be handled in the same amount of time.

Uncertainty and Sensitivity Analysis

Generally, an analyst may not know the exact range of values for a giveninput and must instead make an uncertain guess. Uncertainty analysiscomprises the quantification of how uncertainty of the inputs 1401A-Dinfluences the uncertainty of the outputs 1403A-B. Sensitivity analysisidentifies how uncertainty in an output 1403A-B can be allocated to theuncertainty of input parameters 1401A-D in a process or model.Uncertainty analysis may generally be thought of as a “bottom-up”assessment of data character whereas sensitivity analysis comprises a“top-down” assessment. While an analyst could measure uncertainty from asimplistic topology such as FIG. 14, certain of the present embodimentscontemplate a hierarchical arrangement of the data inputs to betterdetermine their relations to one another and to the outputs AA03A-B.Uncertainty may be characterized using derivatives, intervals, variance,etc. or any other varying quantity. In some embodiments, uncertainty andsensitivity analysis may comprise one of three approaches: parameterscreening, local sensitivity methods and global methods. Each of theseapproaches differ in their complexity and accuracy.

Parameter screening is a coarse one parameter at a time (OAT) approachthat investigates extreme values of the parameters and quicklyidentifies how they influence the output by ranking them in order ofimportance. This method is good for studying models with a few uncertainparameters.

Local sensitivity methods use numerical approximations of localderivatives between the output and input to estimate parametersensitivity. There are a few different approaches to calculate thisderivative (finite difference, direct methods, using Green functions,etc.), but each method typically requires OAT sampling. Again, thismethod is good for studying a small number of uncertain parameters. Asthe name implies, local methods obtain only approximate sensitivityresults at different locations in the sampled space.

In contrast, global methods calculate how the variance of the outputvaries due to the entire sampled range of the parameter space. Unlikelocal methods, the global approach does not assume linearity ormonotonicity in the data or the process which produces it. The Morrismethod is one example of a global SA approach wherein randomizedmatrices are constructed with one parameter varying at a time.Derivative-based global sensitivity can be calculated from functionssuch as

$\begin{matrix}{\mu_{m} = {{\int\left| \frac{\partial f}{\partial x_{m}} \middle| {{x}\mspace{14mu} {or}\mspace{14mu} v_{m}} \right.} = {\int\left| \frac{\partial f}{\partial x_{m}} \middle| {}_{2}{x} \right.}}} & (15)\end{matrix}$

Where the integration is performed over all dimensions of the samplingpoints. Analysis of variance (ANOVA) and other sensitivities may be usedto calculate the uncertainty.

FIG. 16 illustrates a decomposition hierarchy of the energy efficiencyvariable “Facility Electricity” 1602. Outputs may alternatively comprisevalues such as domestic hot water energy, air conditioning usage,electricity usage for a particular room, pump, fan, lighting system,chiller, cooling system etc. Intermediate variables 1603A-E mayrepresent components contributing to the energy consumption of theenergy efficiency variable “Facility Electricity” 1602. The system maybe further broken down into variables 1604 which in turn influence eachof the variables 1603A-E. The illustrated breakdown may be created by ananalyst or building designer based on their intuitive understanding ofthe component relations and their expectations for the building'soperations. The right-most node is the electricity use at the buildinglevel.

By iterating through the value ranges of variables at one level andassessing the effect on variables at a higher level, (for example,iterating through values for variable 1604 and assessing the effect onthe variables 1603A-E) a sensitivity web, illustrated in FIG. 17 may begenerated. The web of FIG. 17 comprises four decomposition levels ratherthan the three of FIG. 17 and also addresses hot water consumptionrather than facility electricity.

In FIG. 17, the nodes are subsystem energy variables, which aredescribed in Table 1, and the connecting wires are sensitivity indices.

TABLE 1 Example parameter types selected for decomposition analysisDecomposition level Type Examples 1 Heating source District heatingsystem (normal capacity, maximum hot water system temperature, loop flowrate, etc.) 2 Cooling source Air cooled chiller (chiller referencecapacity, reference COP, reference leaving chilled water temperature,etc.) 3 (Air Handling AHU (supply air temperature setpoint, cooling coildesign flow rate, Unit) AHU design inlet water temperature, design inletair temperature, etc.) 4 Primary mover: Fans (efficiency, pressure rise,etc.) air loop 5 Primary mover: Pumps (rated flow rate, rated head,rated power consumption, etc.) water loop 6 Terminal unit VAV boxes(maximum air flow rate, minimum air flow fraction, etc.), maximum zonalflow rates 7 Zone external Building envelope (material thermalproperties such as conductivity, density, and specific heat, windowthermal and optic properties, etc.), outdoor conditions (groundtemperature, ground reflectance, etc.) 8 Zone internal Internal heatgains design level (lighting load, number of people, people activitylevel, etc.), schedules 9 Zone setpoint Zone temperature setpoint (spacecooling and heating setpoints) 10 Domestic hot Domestic hot water usage(peak flow rate, target temperature, etc.) water

The circles drawn around each of the nodes represent the coefficient ofvariation. In some embodiments the scales for the circles are arbitraryand are instead intended to be viewed relative to other circles in thefigure. The circles around the nodes illustrate the uncertainty in eachnode, while the edges between the nodes illustrate the influence betweenthe nodes. The thickness of the wires corresponds to the magnitude ofthe sensitivity index. Thicker edges indicate more influence, whilethinner edges indicate less influence. These edges are referred to as“sensitivity indices”. Where there is no wire, the sensitivity index isnegligible, and conversely the thickest wires represent the strongestinfluence between the variables.

In certain embodiments the system generates the web 1700 by firstiterating through each decomposition level of FIG. 16 (from left toright) and performing an uncertainty analysis for each output based onthe collection of inputs (thereby generating the circles 1704A-B). Oncethe uncertainty analysis is complete, the system may then calculate thesensitivity indices 1703A-B. Once the uncertainty analyses have beenperformed for each level and the corresponding circles generated, thesystem may then perform a sensitivity analysis to determine the wirethickness between each component.

Certain embodiments contemplate an improved approach for simulatingbuilding dynamics, by integrating various of the above techniques. Inthese embodiments, quasi-random sampling may be used to generate theparameter samples. A response surface may then be calculated usingsupport vector regression using Gaussian kernels. ANOVA and L2 normderivative-based sensitivities may then be calculated. In someembodiments, only L1 norm (mm) derivative-based sensitivities arepresented.

Summary of Certain Sensitivity Embodiments

FIG. 18 is a logical flow diagram generally describing sensitivityanalysis as used in certain embodiments. In these embodiments, thesystem begins 1801 by acquiring the physical field data from thebuilding 1802. As mentioned, the building may be either real orsynthetic and the sensor data real or simulated or comprising acombination of the two. The system or user may then formulate aninput-output map 1803 for the building. For example, the system or usermay specify the components of the decomposition hierarchy describedabove with respect to FIG. 16. Such a selection may be based onproperties of the building architecture or assumed relationships betweenbuilding components. Although described here in this order, one mayreadily recognize that the data acquired 1802 may be chosen based on theinput-output map generated 1803. The system may then use the samplingmethod, such as the quasi-random methods discussed above, to determinethe optimal input parameter value 1804. The optimal input parametervalue may be used to determine if stop condition 1805 has beensatisfied. For example, if the selected input reduces the real-world ormodeled inefficiency below a specified level, the system may stop 1806or delay further action. Conversely, if the building has not yet reacheda desired operation the process may be repeated. Further discussion ofuncertainty and sensitivity analysis may be found in “Coupled NonlinearDynamical Systems: Asymptotic Behavior and Uncertainty Propagation”,Igor Mezic, 43^(rd) IEEE Conference on Decision and Control. Dec. 14-17,2004 incorporated herein by reference and in “Uncertainty Analysis andSensitivity Decomposition of Building Energy Models” Eisenhower, et al.,Journal of Building Performance Simulation, Vol. 4, May 10, 2011,incorporated by reference herein.

Merged Koopman-Based Decomposition and Visualization

In lieu or in conjunction with the hierarchical decompositions discussedabove, certain embodiments contemplate decomposition hierarchies whichintegrate aspects of the energy 810 or spectral 820 analysis methodsinto their structure. For example, with reference to FIG. 19, certainembodiments contemplate applying the decomposition framework discussedabove with regard to the results of the Koopman-based analysis. Asillustrated in FIG. 19, the first 1901 a, second 1901 b, third 1901 c,and fourth 1901 d order frequency components from the Koopman analysismay be hierarchically organized and the relations therebetween whichaffect a physical field of interest determined using the methodsdiscussed above. Such an approach may be used in conjunction with thedecomposition of FIG. 17 to determine correlations between hierarchicallevels of decomposition and components of the frequency-based analysis.Other applications of spectral techniques in the context of uncertaintyand sensitivity analysis may be found in “Spectral Balance: A FrequencyDomain Framework for Analysis of Nonlinear Dynamical Systems”, Banaszuket al., 43^(rd) IEEE Conference on Decision and Control, Dec. 14-17,2004, incorporated herein by reference.

Integrated Whole-Building Design and Operation—GloBEMS

The methods above are preferably combined to provide an integratedsystem-wide design and operation methodology for the building. Asdiscussed above, the spectral-spatial decomposition may be used on bothraw building system data from an operating building, and upon modeldata. Furthermore, the propagation presented in FIG. 2 may be performednot only on model data but upon data from a building in operation aswell.

As such, the combined portions of this method offer an approach forfault diagnosis and system-wide optimization of the building providingthe most energy efficient design and operation approach available.

The global building energy management system provides a detailedvisualization of energy use and waste, as well as clear, actionableintelligence that can be implemented with resultant energy savings. Theglobal building energy management system also allows for a real-time,immediate determination of a return on investment for all energydecisions, e.g., upgraded equipment, additional management tools, etc.,and enables significant energy savings within a single building orintra-building usage.

The use of the global building energy management system also allows foran analysis of how a building “breathes,” i.e., where energy escapesfrom walls, where heat is lost or maintained, etc., which in turn leadsto corrective actions for such energy loss. Further, the global buildingenergy management system can be implemented in real-time to see how anycorrective actions are working, extract correlations between spatialdistribution of physical fields (that include temperature, humidity,airflow, pressure, people occupancy, plug load density, light intensity)and time-periodic patterns caused by building usage patterns, diurnalcycles and control system cycles, and based on such correlations providemethods for analysis that allow for more efficient use of energy withina structure.

The global building energy management system is enabled by algorithmsthat are tailored for analysis of large parameter dependent systems thatcontain many sensor-based output variables. Because of this, theapproach allows the present invention to be orders of magnitude fasterthan the currently deployed attempts at optimization. Further, theglobal building energy management system takes into account a number ofsensor generated data values that are orders of magnitude larger thannumbers in current use, which allows for the accuracy of the system tobe customer-specified rather than building design specified. Theaccuracy of the sensitivity analysis in the present invention has beenshown to be on the order of 1 millionth of an energy unit, which is farsmaller than current standards and deployed analysis tools.

The global building energy management system also allows forcomprehensive situational analysis of large building energy systems,which includes initial energy audits, monthly updates of the audits,real-time monitoring and control via continuous commissioning throughthe building management system, as well as allowing building management,ownership, engineering or energy consulting firms to analyze and providesolutions for commercial buildings and complexes.

As used herein, “instructions” refer to computer-implemented steps forprocessing information in the system. Instructions can be implemented insoftware, firmware or hardware and include any type of programmed stepundertaken by components of the system.

A “microprocessor” or “processor” may be any conventional generalpurpose single- or multi-core microprocessor such as a Pentium®processor, Intel® Core™, a 8051 processor, a MIPS® processor, or anALPHA® processor. In addition, the microprocessor may be anyconventional special purpose microprocessor such as a digital signalprocessor or a graphics processor. A “processor” may also refer to, butis not limited to, microcontrollers, field programmable gate arrays(FPGAs), application-specific integrated circuits (ASICs), complexprogrammable logic devices (CPLDs), programmable logic arrays (PLAs),microprocessors, or other similar processing devices.

The system is comprised of various modules as discussed in detail below.As can be appreciated by one of ordinary skill in the art, each of themodules comprises various sub-routines, procedures, definitionalstatements and macros. Each of the modules are typically separatelycompiled and linked into a single executable program. Therefore, thefollowing description of each of the modules is used for convenience todescribe the functionality of the preferred system. Thus, the processesthat are undergone by each of the modules may be arbitrarilyredistributed to one of the other modules, combined together in a singlemodule, or made available in, for example, a shareable dynamic linklibrary.

Certain embodiments of the system may be used in connection with variousoperating systems such as SNOW LEOPARD®, iOS®, LINUX, UNIX or MICROSOFTWINDOWS®.

Certain embodiments of the system may be written in any conventionalprogramming language such as assembly, C, C++, BASIC, Pascal, or Java,and run under a conventional operating system.

In addition, the modules or instructions may be stored onto one or moreprogrammable storage devices, such as FLASH drives, CD-ROMs, hard disks,and DVDs. One embodiment includes a programmable storage device havinginstructions stored thereon.

While the above processes and methods are described above as includingcertain steps and are described in a particular order, it should berecognized that these processes and methods may include additional stepsor may omit some of the steps described. Further, each of the steps ofthe processes does not necessarily need to be performed in the order itis described.

While the above description has shown, described, and pointed out novelfeatures of the invention as applied to various embodiments, it will beunderstood that various omissions, substitutions, and changes in theform and details of the system or process illustrated may be made bythose skilled in the art without departing from the spirit of theinvention. As will be recognized, the present invention may be embodiedwithin a form that does not provide all of the features and benefits setforth herein, as some features may be used or practiced separately fromothers.

The steps of a method or algorithm described in connection with theembodiments disclosed herein may be embodied directly in hardware, in asoftware module executed by a processor, or in a combination of the two.A software module may reside in RAM memory, flash memory, ROM memory,EPROM memory, EEPROM memory, registers, hard disk, a removable disk, aCD-ROM, or any other form of storage medium known in the art. Anexemplary storage medium may be coupled to the processor such theprocessor can read information from, and write information to, thestorage medium. In the alternative, the storage medium may be integralto the processor. The processor and the storage medium may reside in anASIC. The ASIC may reside in a user terminal. In the alternative, theprocessor and the storage medium may reside as discrete components in auser terminal.

All of the processes described above may be embodied in, and fullyautomated via, software code modules executed by one or more generalpurpose or special purpose computers or processors. The code modules maybe stored on any type of computer-readable medium or other computerstorage device or collection of storage devices. Some or all of themethods may alternatively be embodied in specialized computer hardware.

All of the methods and tasks described herein may be performed and fullyautomated by a computer system. The computer system may, in some cases,include multiple distinct computers or computing devices (e.g., physicalservers, workstations, storage arrays, etc.) that communicate andinteroperate over a network to perform the described functions. Eachsuch computing device typically includes a processor (or multipleprocessors or circuitry or collection of circuits, e.g. a module) thatexecutes program instructions or modules stored in a memory or othernon-transitory computer-readable storage medium. The various functionsdisclosed herein may be embodied in such program instructions, althoughsome or all of the disclosed functions may alternatively be implementedin application-specific circuitry (e.g., ASICs or FPGAs) of the computersystem. Where the computer system includes multiple computing devices,these devices may, but need not, be co-located. The results of thedisclosed methods and tasks may be persistently stored by transformingphysical storage devices, such as solid state memory chips and/ormagnetic disks, into a different state.

What is claimed is:
 1. A method for analyzing building sensor data, themethod comprising: receiving building sensor data, the building sensordata comprising a plurality of values measured by a plurality ofsensors; determining phase and magnitude values associated with one ormore sensors of the plurality of sensors based on a spectral analysistechnique applied to the building sensor data; and determining a time toactivate or to deactivate an actuator based on at least one of the phaseor magnitude values associated with the one or more sensors, the methodperformed by a building energy management system comprising one or morecomputing devices.
 2. The method of claim 1, further comprisingdetermining energy values associated with the one or more sensors basedon an energy-based technique applied to the building sensor data.
 3. Themethod of claim 2, wherein determining a time to activate or todeactivate an actuator further comprises determining a time to activateor to deactivate an actuator based on at least one of the phase,magnitude, or energy values associated with the one or more sensors. 4.The method of claim 2, further comprising generating a visualizationbased on at least one of the phase, magnitude, or energy valuesassociated with the one or more sensors, the visualization comprising anoverlay upon a building schematic, the overlay depicting at least one ofthe phase, magnitude, or energy values associated with the one or moresensors.
 5. The method of claim 2, wherein the energy-based techniquecomprises a Proper Orthogonal Decomposition.
 6. The method of claim 1,wherein the spectral analysis technique comprises a Koopman-basedtechnique.
 7. The method of claim 1, wherein the building sensor datacomprises data from at least one of a real-world building or a simulatedmodel of a building.
 8. The method of claim 1, wherein the plurality ofvalues comprise one of temperature values, humidity values, airflowvalues, pressure values, people occupancy values, plug load densityvalues, or light intensity values.
 9. The method of claim 1, furthercomprising: identifying a final output based on at least one of thephase or magnitude values; identifying a plurality of inputs affectingthe final output based on the at least one of the phase or magnitudevalues; and generating a graph for display, the graph comprising an edgebetween a first input in the plurality of inputs the final output,wherein a magnitude of the edge corresponds to an influence of the firstinput on the final output.
 10. An electronic apparatus for assessingbuilding properties comprising: a memory configured to store a data set,the data set comprising building sensor data, the building sensor datacomprising a plurality of values measured by a plurality of sensors; andone or more processors, the memory further configured to storeinstructions that, when executed by the one or more processors,implement a process comprising: determining phase and magnitude valuesassociated with one or more sensors of the plurality of sensors based ona spectral analysis technique applied to the building sensor data, anddetermining a time to activate or to deactivate an actuator based on atleast one of the phase or magnitude values associated with the one ormore sensors.
 11. The electronic apparatus of claim 10, wherein thememory is further configured to store instructions that, when executedby the one or more processors, implement a process comprisingdetermining energy values associated with the one or more sensors basedon an energy-based technique applied to the building sensor data. 12.The electronic apparatus of claim 11, wherein the memory is furtherconfigured to store instructions that, when executed by the one or moreprocessors, implement a process comprising determining a time toactivate or to deactivate an actuator based on at least one of thephase, magnitude, or energy values associated with the one or moresensors.
 13. The electronic apparatus of claim 11, wherein the memory isfurther configured to store instructions that, when executed by the oneor more processors, implement a process comprising generating avisualization based on at least one of the phase, magnitude, or energyvalues associated with the one or more sensors, the visualizationcomprising an overlay upon a building schematic, the overlay depictingat least one of the phase, magnitude, or energy values associated withthe one or more sensors.
 14. The electronic apparatus of claim 11,wherein the energy-based technique comprises a Proper OrthogonalDecomposition.
 15. The electronic apparatus of claim 10, wherein thespectral analysis technique comprises a Koopman-based technique.
 16. Theelectronic apparatus of claim 10, wherein the plurality of valuescomprise one of temperature values, humidity values, airflow values,pressure values, people occupancy values, plug load density values, orlight intensity values.
 17. A non-transitory computer storage comprisinginstructions that direct a computing system comprising one or morecomputing devices to perform a process that comprises: receivingbuilding sensor data, the building sensor data comprising a plurality ofvalues measured by a plurality of sensors; determining phase andmagnitude values associated with one or more sensors of the plurality ofsensors based on a spectral analysis technique applied to the buildingsensor data; and determining a time to activate or to deactivate anactuator based on at least one of the phase or magnitude valuesassociated with the one or more sensors.
 18. The non-transitory computerstorage of claim 17, wherein the instructions further direct thecomputing system to perform a process that comprises determining energyvalues associated with the one or more sensors based on an energy-basedtechnique applied to the building sensor data.
 19. The non-transitorycomputer storage of claim 18, wherein the instructions further directthe computing system to perform a process that comprises determining atime to activate or to deactivate an actuator based on at least one ofthe phase, magnitude, or energy values associated with the one or moresensors.
 20. The non-transitory computer storage of claim 18, whereinthe instructions further direct the computing system to perform aprocess that comprises generating a visualization based on at least oneof the phase, magnitude, or energy values associated with the one ormore sensors, the visualization comprising an overlay upon a buildingschematic, the overlay depicting at least one of the phase, magnitude,or energy values associated with the one or more sensors.